洪宏基2006-07-252018-07-092006-07-252018-07-092000http://ntur.lib.ntu.edu.tw//handle/246246/2691The project employed a group-theoretical ap- proach to investigate constitutive models of elastoplasticity. In the axial-torsional test, the hoop and radial strains are usually not known a priori; hence, in the constitutive model simula- tion of the responses they can not be viewed as inputs. This greatly complicates the constitutive analyses because the resulting differential con- stitutive equations become highly nonlinear. To tackle this diffculty we convert the highly nonlin- ear axial-torsional problem of perfect elastoplas- ticity to a quasi-linear system _X = A(X; t)X, where A(X; t) 2 sl(2; 1;R) is a local Lie algebra of the special pseudo-linear group SL(2; 1;R). The underlying space of this problem is found to be a pseudo-Riemann manifold which is lo- cally pseudo-Euclidean space E3 2;1 with the metric indefinite and also dependent on the time com- ponent. Utilizing the internal symmetry group, we can consequently develop a highly accurate group-preserving scheme, which guarantees the fulfillment of the consistency condition in every time marching of the calculations. The axial-torsional test equipment MTS809 of the NTU College of Engineering and the pressure control machine was used to study the cyclic and ratchetting behavior of tubular specimens of Al- 7075 and stainless steel 316. We also studied contraction ratios experimen- tally, one rate form and one total form under dif- ferent initial values of the specimens. The values of both contraction ratios may be greater than 1=2. Moreover, for some cases we found that the rate form contraction ratio exceeds the value 1.application/pdf617348 bytesapplication/pdfzh-TW國立臺灣大學土木工程學系暨研究所塑性偽黎曼流形特殊線性群軸扭雙向循環實驗收縮比plasticitypseudo-Riemann manifoldspecial pseudo-linear groupaxial-torsional cyclic testcontraction ratioreporthttp://ntur.lib.ntu.edu.tw/bitstream/246246/2691/1/892211E002032.pdf